The Routh Hurwitz Criteria for Studying The Stability and Bifurcation in Multispiral Chua Chaotic Attractor

Malika Belouerghi; Tidjani Menacer; René Lozi

doi:10.13164/mendel.2023.1.071

Malika Belouerghi Laboratory of Applied Mathematics, University Mohamed Khider of Biskra, P.O. Box 145, Biskra 07000, Algeria
Tidjani Menacer University Mohemed Khider Biskra, Algeria
René Lozi University Cˆote d’Azur, CNRS, LJAD, France, Parc Valrose 06108, Nice C´edex 02

DOI: https://doi.org/10.13164/mendel.2023.1.071

Keywords: Bifurcation, Chua’s Circuit, Hidden Attractor, Hidden Bifurcation, Stability

Abstract

This article discusses the multispiral Chua Chaotic attractor’s hidden bifurcations that are generated by the sine function. The number of spirals (also known as a multiscroll attractor) that are controlled by the integer parameter c can be used to describe the basic shape of chaotic attractors. Since this parameter is an integer, increasing it by one does not allow the observation of bifurcations from n to n + 2 spirals. The method of hidden bifurcations, however, enables the observation of such bifurcations by adding a real parameter ε. Chaotic attractors with either an even or an odd number of spirals are visible along the marked paths of bifurcation. Moreover, this additional hidden parameter allows finding the bifurcation of the multispiral Chua attractor from a stable state to a chaotic state. Furthermore, the Routh-Hurwitz criteria are used to study the stability of the original equilibrium point of the Chua attractor.

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